Given $ m \angle LOM = 3x + 74$, and $ m \angle MON = 8x + 95$, find $m\angle MON$. $O$ $L$ $N$ $M$
Answer: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {3x + 74} + {8x + 95} = {180}$ Combine like terms: $ 11x + 169 = 180$ Subtract $169$ from both sides: $ 11x = 11$ Divide both sides by $11$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 8({1}) + 95$ Simplify: $ {m\angle MON = 8 + 95}$ So ${m\angle MON = 103}$.